I recently acquired a Jet mini lathe and have always heard they are a great machine for rod building purposes. However, I have no idea what I need on it to be able to accommodate steel mandrels for turning cork. I know some sort of self-centering chuck, but where might I find such an animal?

You can also get chucks at your local Woodcraft or Rockler store, if you have one of those close by. When you get a chuck, make sure the jaws will hold all of your mandrels. Some of the standard chucks don't come with jaws that reduce small enough to hold the 1/4" mandrels.